First slide

Introduction to mathematical reasoning

Question

The statement $p \to (q \to p)$ is equivalent to

Easy

A

$p \to (p \to q)$
B

$p \to (p \lor q)$
C

$p \to (p \land q)$
D

$p \to (p \leftrightarrow q)$

Solution

$\begin{array}{l} p \to (q \to p) \equiv\sim p \lor (q \to p) \\ \equiv (~ p) \lor (~ q \lor p) \\ \equiv (~ q) \lor (p \lor ~ p) \\ \equiv (~ q) \lor T = T \end{array}$
$∴ p \to (q \to p)$ is a tautology.
Also
$\begin{aligned} p \to (p \lor q) \equiv\sim p \lor (p \lor q) \\ \equiv (~ p \lor p) \lor q \equiv T \lor q = T \end{aligned}$
$∴ ρ \to (p \lor q)$ ) is also a tautology
Thus, $p \to (q \to p)$ is equivalent to $p \to (p \lor q)$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App